Present Value with Constant Perpetual Growth Rate
Present value with constant perpetual growth rate is often applied to find present value or current price of ordinary share (common stock).
- C0 : base amount at the beginning of period 1 (Period 0) for constant perpetual growth rate
- g: constant perpetual growth rate
The XYZ Co. has just paid a cash dividend of $2 per share. Potential investors require a 16 percent return from investments. If the dividend is expected to grow at a steady 8 percent per year, what is the current value of the stock? What will the stock be worth in five years?
- The current value of the stock
So current price =$27
- Stock price at the next five years
Dividend in five year
=> D5 =Do*(1+g)5 =$2*(1+0.08)5 =$2.9387, so price of stock in five years:
=>P5 = D5 *(1+g)/(r-g)
= $2.9387 *(1+0.08)/(0.16-0.08)=$39.67 or
P5 = Po*(1+g)5 =$27 *(1+0.08)5 =$39.67